Title: On-the-fly graph-theoretical basin generation method for kinetic Monte Carlo approaches

This study addresses the inefficiencies that arise in kinetic Monte Carlo (KMC) simulations when the system kinetics are dominated by low-energy obstacles, resulting in a tiny increase in computation time per step. In particular, these obstacles manifest as 'flickers' — collections of states separated by low-energy barriers within an energy basin— and have negligible impact on system evolution. To circumvent this, we introduce the local basin approach based on graph-theoretical classification using NAUTY [1] that allows the on-the-fly construction and reconstruction of local basins. The approach, which is implemented in the kART,  an off-lattice kinetic Monte Carlo algorithm with on-the-fly catalog building, enables the analytical computation of statistically accurate analytical solutions for the interconnected flickering states and their escape rates as the energy landscape is explored. This solution is based on the evaluation of mean-residence time using the basin-auto-constructing Mean Rate Method (bac-MRM) [2], an approach that resembles a master equation and categorizes the energetic landscape into basin and non-basin states. This presentation addresses the implementation of local basin kART simulations that seamlessly incorporate local basin and non-basin events. We also examine the temporal distribution of basin escapes and the dynamic interplay between basin and non-basin states.

 

[1] McKay, Brendan D. "Practical graph isomorphism." (1981): 45-87.

[2] Puchala, Brian, Michael L. Falk, and Krishna Garikipati. "An energy basin finding algorithm for kinetic Monte Carlo acceleration." The Journal of chemical physics 132.13 (2010).